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Atypical bifurcation for periodic solutions of ϕ-Laplacian systems

Part of: Boundary value problems Nonlinear operators and their properties Qualitative theory Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  03 September 2025

Pierluigi Benevieri  and
Guglielmo Feltrin
Pierluigi Benevieri*
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, São Paulo, SP - CEP 05508-090, Brazil (pluigi@ime.usp.br)
Guglielmo Feltrin
Affiliation:
Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università degli Studi di Udine, Via delle Scienze 206, Udine 33100, Italy (guglielmo.feltrin@uniud.it)
*
*Corresponding author.
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Abstract

In this paper, we study the T-periodic solutions of the parameter-dependent ϕ-Laplacian equation

\begin{equation*}(\phi(x'))'=F(\lambda,t,x,x').\end{equation*}

Based on the topological degree theory, we present some atypical bifurcation results in the sense of Prodi–Ambrosetti, i.e., bifurcation of T-periodic solutions from λ = 0. Finally, we propose some applications to Liénard-type equations.

Dedicated to Professor Maria Patrizia Pera on the occasion of her 70th birthday

Keywords

atypical bifurcationdegree theoryϕ-Laplacian operatorperiodic solutionsLiénard equations

MSC classification

Primary: 34B15: Nonlinear boundary value problems
Secondary: 34C23: Bifurcation 34C25: Periodic solutions 47H11: Degree theory 47J05: Equations involving nonlinear operators (general)

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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